As the remnant radio galaxy ages, its electrons will lose so much energy that their spectra will eventually steepen. This steepening would reach to a point where they do not emit significant radiation at high frequencies, instead, the radio emission may only be observable at low frequencies.
However, [1]} argues that in addition to the aged population of remnant radio galaxies, there should be younger population as well in which lobes have not had time to steepen over the observed frequency range [2]}, [3]}.
It is possible that the remnant phase of a radio galaxy is governed by a Sedov-like expansion, which will cause the dimming of radio emission due to a decrease in the magnetic field strength and a decrease in particle energies due to adiabatic expansion losses. Unfortunately, the models of the spectra of remnant radio galaxy are highly degenerate, and the modeling of an individual remnant radio galaxy cannot constrain the remnant phase of radio galaxy [4]}.
Therefore, a possible way to constrain the remnant phase is via a statistical approach, and sadly, due to their small number, the physics of remnant radio galaxies remains poorly understood.
Of course, alongside their must exist a significant population of remnant radio galaxies, which show the absence of detectable radio emission in many clusters associated with merger activity [5]}.
Thus, searching for low-surface-brightness profiles, say \(\lesssim \)  50 mJy arcmin\(^{-2}\) , with an absence of radio cores and hotspots, and with no well-defined radio morphologies, is a possible way to identify remnant radio sources in large survey images.
